A hemispherical dome of a building needs to be painted.

Question:

A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is $17.6 \mathrm{~cm}$, find the cost of painting it, given the cost of painting is Rs.5 per $100 \mathrm{~cm}^{2}$

Solution:

Given that only the rounded surface of the dome to be painted, we would need to find the curved surface area of the hemisphere to know the extent of painting that needs to be done.

Now, circumference of the dome = 17.6 cm

Therefore 2πr = 17.6

2 × 22/7 × r = 17.6 m

So, the radius of the dome $=2 \pi r^{2}$

= 2 × 22/7 × 2.8 × 2.8

$=49.28 \mathrm{~m}^{2}$

Cost of painting $100 \mathrm{~cm}^{2}$ is Rs. 5

So, the cost of painting $1 \mathrm{~m}^{2}=$ Rs. 500

Therefore the cost of painting the whole dome = Rs. 500 × 49.28

= Rs. 24640